Pythagoras Revived: Mathematics and Philosophy in Late Antiquity

Pythagoras Revived: Mathematics and Philosophy in Late Antiquity

Dominic J. O'Meara

Language: English

Pages: 264


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The Pythagorean idea that number is the key to understanding reality inspired philosophers in the fourth and fifth centuries to develop theories in physics and metaphysics using mathematical models. These theories were to become influential in medieval and early modern philosophy, yet until now, they have not received the serious attention they deserve. This book marks a breakthrough in our understanding of the subject by examining two themes in conjunction for the first time: the figure of Pythagoras as interpreted by the Neoplatonist philosophers of the period, and the use of mathematical ideas in physics and metaphysics.

Part I The Revival Of Pythagoreanism In the Neoplatonic School
1.Varieties of Pythagoreanism in the Second and Third Centuries AD
1. Numenius of Apamea
2. Nicomachus of Gerasa
3. Anatolius
4. Porphyry

2. Iamblichus' Work On Pythagoreanism: Title, Plan, the First Four Books
1. The Title and Overall Plan
2. Pythagoras (Book I: On the Pythagorean Life)
3. Pythagorean Philosophy (Book II: the Protreptic)
4. Pythagorean Mathematical Science (Book III: On General Mathematical Science)
5. Arithmetic (Book IV: On Nicomachus' Arithmetical Introduction)

3. On Pythagoreanism V – VII: The Excerpts in Michael Psellus
1. Michael Psellus, Philosophical Excerptor
2. Psellus' Excerpts from On Pythagoreanism V – VII
3. On Pythagoreanism V
(i) General Plan
(ii) Physical Number
(iii) Formal and Material Causation
(iv) Efficient Causation
(v) Change
(vi) Place
(vii) The Void
(viii) Conclusion

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relation to the divine, his privileged access to intelligible truths, and his soteriological mission. The Pythagorean legend, in serving to recommend to the reader Pythagoras' special claim to divine insight, also promotes that insight, namely the philosophy and sciences associated with Pythagoras. In short, On the Pythagorean Life is a protreptic to Pythagorean philosophy through an illustration of the spiritual credentials of the founder of that philosophy. The later chapters accomplish

intention simply to reproduce Nicomachus' Introduction, adding, subtracting, changing nothing.154 As a matter of fact this claim is not verified by what follows. 153 Cf. above, n. 46. 154 5, 15–25, where Iamblichus also denies any intention to introduce foreign matters (καινά); he will reproduce only the opinions of the ‘ancients’. This might be compared to Numenius' ban on καινοτομία. Numenius may also be the inspiration of Iamblichus' stress on the purity of Nicomachus' Pythagoreanism. 52

extraneous (ἐπɛίσακτος) local situation.196 The connatural ‘proper ordering’ has an organizing, preserving function recalling that given to place by Iamblichus as reported by Simplicius.197 In Psellus' excerpts numbers are said to have place as ‘containing’ bodies in their power, a causal rather than a local ‘enclosing’. If numbers ‘contain’ bodies in this sense, then they also ‘contain’ a connatural part of bodies, namely place (81–4). The excerpts also ascribe to numbers place in a different

mediator between material and immaterial reality. This position does not rule out, of course, the use of the ‘images’ of arithmetic, but it does represent a shift in fulcrum: the role that Iamblichus gives arithmetic in On Pythagoreanism both as an introductory and as a pivotal science—Books V–VII are after all concerned with arithmetic reaching down into physics and ethics and up into metaphysics—is assigned in Proclus rather to geometry. One might also speak of a change from Iamblichus'

which mathematical truths can be applied ‘downwards’ and ‘upwards’. In revising, clarifying, and documenting Iamblichus, Proclus largely replaces the Pythagorean authorities in Iamblichus with texts taken from Plato. This appears to relate not only to Proclus' view of Euclid's Elements as a manual of Platonic geometry, but also to his tendency to regard Plato as more ‘scientific’ than the Pythagoreans. The comparison between Proclus and Iamblichus also indicates that Proclus chose geometry to

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